Let T be a rooted, multi-type Galton-Watson (MGW) tree of finitely many types with at least one offspring at each vertex and an offspring distribution with exponential tails. The r-biased random walk X(t) on T is the nearest neighbor random walk which, when at a vertex v with d(v) offspring, moves closer to the root with probability r/(r+d(v)) and to each of the offspring with probability 1/(r+d(v)). This walk is transient if and only if 0<r<R, with R the Perron-Frobenius eigenvalue for the (assumed) irreducible matrix of expected offspring numbers. Following the approach of Peres and Zeitouni (2008), we show that at the critical value r=R, for almost every T, the process |X(nt)|/sqrt(n) converges in law as n goes to infinity to a deterministic positive multiple of a reflected Brownian motion. Our proof is based on a new explicit description of a reversing measure for this walk from the point of view of the particle, a construction which extends to the reversing measure for a biased random walk with random environment

(RWRE) on MGW trees, again at a critical value of the bias.